Problem: Simplify the following expression: $ n = \dfrac{2}{-7z - 5} - \dfrac{-1}{2} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{2}{-7z - 5} \times \dfrac{2}{2} = \dfrac{4}{-14z - 10} $ Multiply the second expression by $\dfrac{-7z - 5}{-7z - 5}$ $ \dfrac{-1}{2} \times \dfrac{-7z - 5}{-7z - 5} = \dfrac{7z + 5}{-14z - 10} $ Therefore $ n = \dfrac{4}{-14z - 10} - \dfrac{7z + 5}{-14z - 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{4 - (7z + 5) }{-14z - 10} $ Distribute the negative sign: $n = \dfrac{4 - 7z - 5}{-14z - 10}$ $n = \dfrac{-7z - 1}{-14z - 10}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{7z + 1}{14z + 10}$